# Probability

## Probability

What is probability?

What are the different types of probability?

Define sample space, power set and events

How do you assign probability to an event?

How to denote the probability of an event?

What is the opposite or complement of an event?

What is the joint probability of two events?

What is the probability of independent events?

What is the probability of both the events occurring if they are mutually exclusive?

What is the probability of either of the events occurring if they are mutually exclusive?

What is the probability for not mutually exclusive events?

What are the rules of probability?

Let's Review

### What is probability?

Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur.
A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

Video: Probability for Beginners : Solving Math Problems

### What are the different types of probability?

There are two types of probability, namely Theoretical and Experimental probability.
Theoretical probability = Number of favorable outcomes / Total number of outcomes
Experimental probability = Number of favorable outcomes / Total number of trials
Video: Types of probability

### Define sample space, power set and events

Consider an experiment that can produce a number of results. The collection of all possible results is called the sample space of the experiment. The power set of the sample space is formed by considering all different collections of possible results. For example, rolling a dice can produce six possible results. One collection of possible results gives an odd number on the dice. Thus, the subset {1,3,5} is an element of the power set of the sample space of dice rolls. These collections are called "events". In this case, {1,3,5} is the event that the dice falls on some odd number. If the results that actually occur fall in a given event, the event is said to have occurred.

Video: Experiment, Outcome, Sample space, and event

### How do you assign probability to an event?

A probability is a way of assigning every event a value between zero and one, with the requirement that the event made up of all possible results (in our example, the event {1,2,3,4,5,6}) is assigned a value of one. To qualify as a probability, the assignment of values must satisfy the requirement that if you look at a collection of mutually exclusive events (events with no common results, e.g., the events {1,6}, {3}, and {2,4} are all mutually exclusive), the probability that at least one of the events will occur is given by the sum of the probabilities of all the individual events.

Video: Simple probability

### How to denote the probability of an event?

The probability of an event A is written as .......

### Let's Review

1. ____ is the measure of the likelihood that an event will occur.
2. Probability is quantified as a number between ____ and ____.
3. There are two types of probability, namely ____ and ____ probability.
4. Theoretical probability = Number of favorable outcomes / Total number of ____.
5. Experimental probability = Number of favorable outcomes / Total number of ____.
6. The collection of all possible results is called the ____ ____ of the experiment.
7. The ____ ____ of the sample space is formed by considering all different collections of possible results.
8. The probability of an event A is written as ____ , ____ , or ____ .
9. If two events A and B occur on a single performance of an experiment, this is called the ____ or ____ ____ of A and B, denoted as
10. If two events, A and B are independent then the ____ probability is for example, if two coins are flipped the chance of both being heads is.
11. If two events are mutually exclusive then the probability of ____ occurring is denoted as
12. If two events are mutually exclusive then the probability of ____ occurring is denoted as .  For example, the chance of rolling a 1 or 2 on a six-sided die is

1. Probability is the measure of the likelihood that an event will occur.
2. Probability is quantified as a number between 0 and 1.
3. There are two types of probability, namely Theoretical and Experimental probability.
4. Theoretical probability = Number of favorable outcomes / Total number of outcomes.
5. Experimental probability = Number of favorable outcomes / Total number of trials.
6. The collection of all possible results is called the sample space of the experiment.
7. The power set of the sample space is formed by considering all different collections of possible results.
8. The probability of an event A is written as , or
9. If two events A and B occur on a single performance of an experiment, this is called the intersection or joint probability of A and B, denoted as
10. If two events, A and B are independent then the joint probability is for example, if two coins are flipped the chance of both being heads is.
11. If two events are mutually exclusive then the probability of both occurring is denoted as .
12. If two events are mutually exclusive then the probability of either occurring is denoted as .  For example, the chance of rolling a 1 or 2 on a six-sided die is

NOTE: You need to be subscribed to either a monthly or annual plan to view the full set of Math Lessons (Study Guide)
Please visit  to register for a plan.

Have fun learning!

Related Content: